Related papers: Effect of Correlations Between Model Parameters an…
Current neutrino experiments measure the neutrino mixing parameters with an unprecedented accuracy. The upcoming generation of experiments will be sensitive to subdominant effects that can give information on the unknown neutrino…
A substantial fraction of systematic uncertainties in neutrino oscillation experiments stem from the lack of precision in modeling the nuclear target in neutrino-nucleus interactions. Whilst this has driven significant progress in the…
Experimental research on behavior and cognition frequently rests on stimulus or subject selection where not all characteristics can be fully controlled, even when attempting strict matching. For example, when contrasting patients to…
We analyze the spatio-temporal patterns of two competing species in the presence of two white noise sources: an additive noise acting on the interaction parameter and a multiplicative noise which affects directly the dynamics of the species…
We discuss fitting correlated data - with the example of hadron mass spectroscopy in mind. The main conclusion is that the method of minimising correlated $\chi^2$ is unreliable if the data sample is too small.
Deviations between the form of trajectory assumed in a fit to a set of measurements and the actual form of the trajectory can give rise to sequential correlations in the residuals from the fit. These correlations can provide a more powerful…
We propose a new and rather stringent criterion for testing the goodness of fit between a theory and experiment. It is motivated by the paradox that the criterion on \chi^2 for testing a theory is much weaker than the criterion for finding…
We often estimate a parameter of interest psi when the identifying conditions involve a nuisance parameter theta. Examples from causal inference are Inverse Probability Weighting, Marginal Structural Models and Structural Nested Models. To…
Many experiments are currently looking for evidence of neutrino mass in the form of neutrino oscillations. Oscillation probabilities are non-linear functions of the neutrino mixing matrix elements, so most comparisons of data to theory are…
Mixed-effect models are flexible tools for researchers in a myriad of fields, but that flexibility comes at the cost of complexity and if users are not careful in how their model is specified, they could be making faulty inferences from…
Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…
We study the effect of parameter fluctuations on synchronization of a coupled chaotic system. The fluctuations to the parameter can be random or it can be a periodic modulation. For random fluctuations we introduce a new quantity, the…
Having a sufficient quantity of quality data is a critical enabler of training effective machine learning models. Being able to effectively determine the adequacy of a dataset prior to training and evaluating a model's performance would be…
A popular approach to perform inference on a target parameter in the presence of nuisance parameters is to construct estimating equations that are orthogonal to the nuisance parameters, in the sense that their expected first derivative is…
Many recent studies endeavor to improve open-source language models through imitation learning, and re-training on the synthetic instruction data from state-of-the-art proprietary models like ChatGPT and GPT-4. However, the innate nature of…
We review the status and prospects of theoretical studies of neutrino-nucleus interactions, and discuss the influence of the treatment of nuclear effects on the determination of oscillation parameters. The models developed to describe the…
For finite random systems, it is possible to define two types of variances (noises). It is demonstrated that their ratio is useful in calculating the correlation length of an infinite and rather general random system, as a function of…
Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…
Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…
We derive relations between standard order parameter correlations and the noise correlations in time of flight images, which are valid for systems with long range order as well as low dimensional systems with algebraic decay of…